Prime Minister John Key fired back, pointing out that the rules for foreign trusts were established by the previous Government in 2006.
Those rules were backed by New Zealand First at the time. The Greens abstained from voting.
Mr Key said any trust and its trustees had to be recorded by New Zealand when it was registered.
If any of the 44 countries which New Zealand had tax agreements with requested further information about these trusts, the owners were obliged to provide the information.
"On every occasion where an international Government has asked for that information we have provided it," Mr Key said.
The Inland Revenue Department (IRD) said today it was unable to immediately say how many times foreign jurisdictions had sought details about New Zealand-based trusts. The departments says on its website that it provides information to foreign governments on a case-by-case basis, and subject to confidentiality laws.
Green Party co-leader James Shaw said requiring the owners of trusts to keep records was not the same as disclosing them.
Furthermore, foreign authorities could not seek information on trusts which had not disclosed the owner's name, country or the trust's beneficiaries.
"How do they know what to ask for?" he said.
The leaked documents did not show any illegal activity related to New Zealand trusts. They revealed that a senior Maltese politician and a Mexican business had set up trusts in New Zealand, possibly containing $100 million or more in assets.
Mr Shaw said that even without evidence of illegal activity, the details were damaging New Zealand's reputation as a "clean operator".
Mr Key reiterated today that the OECD had given New Zealand's rules a "clear bill of health" in 2013.
Labour leader Andrew Little said that was not entirely accurate. The OECD said "some improvements to New Zealand's legal and regulatory framework may be needed" and said enforcement powers might not be effective for non-resident directors.
The OECD report said that these gaps would be resolved by anti-money laundering legislation which was proposed at the time.
However, when this legislation was later passed, it excluded trusts.